There'll be a junction box up inside the pin box where the wiring from the 7 way plug is connected to the trailer wiring. Have you checked the 7 way plug on the truck?
You're right...the running and tail lights are off the same feed. Must be a bad connection between the tail light and rear clearance lights. You could check the tail lights first as they're working. I think the tail light lenses are held with tabs on all four sides...need to gently pry outwards. Not sure if you can access the wiring connections from there or whether you have to remove the fixture. You can call GHD Customer Service at 574-825-9679 for some direction.